a. Field of the Invention
The present invention relates to a control system for a magnetic type bearing for floating a high-speed rotating member such as a spindle for use in a turbo-pump, a compressor, a turbine or a machine tool and further a traveling member such as a tenter.
b. Description of the Related Art
Means for floatingly holding a rotating member and a traveling member have utilized a magnetic type bearing employing an electromagnet. The magnetic type bearing has less loss than that of a conventional lubricated hydraulic bearing, maintains a dry, clean atmosphere and in particular is useful under vacuum.
In the magnetic type bearing, in order to establish a float position of the rotating member and the traveling member, there is provided a system in which a position of a floating member is measured to determine a current value flowing in the electromagnet on the basis of the measured signal so that a magnitude of a magnetic force produced from the electromagnet is determined.
Referring to FIG. 7 showing a block diagram illustrating the above manner, a position sensor 11 measures a position (displacement) of the floating member and may be, for example, an eddy current type displacement meter. A position feed-back gain circuit 12 proportionally multiplies a magnitude of a signal obtained by the position sensor 11 to a required magnitude. A control circuit 13 is a processing circuit for converting a signal obtained by the position feed-back gain circuit 12 to a proper signal to supply the signal to an electromagnet 14 and may be, for example, a PID (Proportion, Integration and Differentiation) circuit, a phase compensation circuit or a combination thereof. The electromagnet 14 includes a coil wound on an iron core and produces a magnetic force for floating the member in response to a current supplied from the control circuit 13.
A simple position feed-back system has the control circuit 13 formed of only a proportional element (P element). The transfer function of an input I and a magnetic force F of an output of the electromagnet 14 is given by the following first-order lag system which depends on resistors and inductances of a coil and an iron core. EQU F/I=K.sub.M /(1+T.sub.M .multidot.S) (1)
where K.sub.M is a gain of the electromagnet 14, T.sub.M is a time constant of the electromagnet 14, and S is a Laplacian operator. Accordingly, the transfer function of the force F exerted on the floating member with respect to the displacement D measured by the position feed-back system is as follow: EQU F/D=K.sub.F .multidot.K.sub.P .multidot.K.sub.m /(1+T.sub.M .multidot.S) (2)
where K.sub.F is a proportional gain of the position feed-back gain circuit 12 and K.sub.P is a proportional gain of the control circuit 13. In order to observe a frequency characteristic of the force/displacement (F/D) of the position feed-back system, the Laplacian operator is set to S=j2.pi.f in which f is a frequency (Hz) and j=.sqroot.-1 and is substituted in the equation (2). The force/displacement (F/D) is a complex number as follow: EQU F/D=K.sub.R (f)+j.multidot.K.sub.I (f) (3)
The real part K.sub.R of the force/displacement (F/D) in the above equation (3) means stiffness dependent on the frequency f and an imaginary part K.sub.I thereof means attenuation dependent on the frequency f. The first-order lag as described in the equation (2) has always a negative imaginary part and the attenuation forms an unstabilizing force for the floating member.
FIG. 8 is a graph showing a relation of the force/displacement (F/D), that is, a relation of a value of the imaginary part of the equation (3) and the frequency f. A dashed line A shown in FIG. 8 corresponds to the equation (2) and shows the above-described state. A characteristic frequency fc determined by the floating member and the position feed-back system increases divergently and the system can not operate due to the attenuation of the characteristic frequency fc, particularly the attenuation of the floating member if a value of the frequency f=fc shown in FIG. 8 is large.
Thus, in order to give the attenuation effect to the force/displacement (F/D) of the position feed-back system, the control circuit 13 comprises a differential element (D element) or a position compensation element disposed in parallel with the proportional element (P element). In this description, the differential element is taken up by way of example. When the differential element (D element) is added to the control circuit 13, the following first-order lag is added to the circuit. EQU Differential Element=K.sub.D .multidot.S/(1+T.sub.D .multidot.S) (4)
where K.sub.D is a gain of the differential element and T.sub.D is a time constant. The force/displacement (F/D) of the position feed-back system including only the differential element is as follow: EQU F/D=K.sub.F .multidot.K.sub.D .multidot.K.sub.M .multidot.S/{(1+T.sub.D .multidot.S)(1+T.sub.M .multidot.S)} (5)
Since the numerator of the equation (5) is an equation of a first degree of S and the denominator thereof is an equation of a second degree of S, the imaginary part of the equation (5) is given by a one-dot chain line B shown in FIG. 8. That is, the attenuation effect is given to the floating member in a low frequency range and the unstabilizing operation is given to the floating member in a high frequency range. In order to hold the position of the floating member, the control circuit 13 requires both of the proportional element and the differential element. The force/displacement (F/D) of the position feed-back system of the control circuit 13 is given by EQU F/D=K.sub.F .multidot.{K.sub.P +K.sub.D .multidot.S/(1+T.sub.D .multidot.S)}.multidot.K.sub.M /(1+T.sub.M .multidot.S) (6)
The force/displacement (F/D) is also shown by a solid line C of FIG. 8 and has the same characteristic as described above. When the characteristic frequency fc determined by the floating member and the position feed-back system is placed in a low frequency range having the attenuation effect, stabilization can be obtained and operation can be made without occurrence of vibration.
When it is considered that the magnetic type bearing having the above characteristic is employed as a bearing 16 of a rotating member 15 shown in FIG. 9(a) to float the rotating member 15, the following phenomenon occurs. The rotating member 15 has unlimited number of characteristic frequencies the first five of which are shown in FIGS. 9(b), (c), (d), (e) and (f). The attenuation of material of the rotating member 15 itself acts on unstabilization with respect to the characteristic frequency less than a rotational number of the member and acts as the attenuation operation with respect to the characteristic frequency larger than the rotational number.
Accordingly, it is necessary to set the characteristic frequency less than the rotational number within the frequency range in which the attenuation effect of the force/displacement (F/D) of the position feed-back system of the magnetic type bearing is brought. However, since the number of the characteristic frequencies of the rotating member 15 is unlimited as shown in FIGS. 9(b) , (c), (d), (e) and (f), the characteristic frequency certainly exists in the frequency range in which the unstabilizing operation of the force/displacement (F/D) is effected. Accordingly, when the unstabilizing operation of the position feed-back system of the magnetic type bearing is larger than the attenuation of the characteristic frequency by the rotating member 15 itself, operation is destabilized and vibration of the rotating member increases divergently, so that the rotating member can not be rotated.
As described above, heretofore, in order to hold the position of the floating member, the position of the floating member is measured and the measured signal is fed back to produce force from the electromagnet. However, the force is destabilizing force which vibrates the floating member. Thus, even if processing such as the PID and phase compensation is provided in the control circuit 13, the force is the stabilizing force (attenuation) in the low frequency range, while the force still contains a large destabilizing force in a middle and high frequency range. Accordingly, the floating member such as the rotating member having the unlimited number of characteristic frequencies certainly includes the characteristic frequency existing in the frequency range in which the destabilizing force is produced and divergent vibration occurs by means of the magnetic type bearing.